Accurate estimation of occupational performance capability facilitates better job (re-) design by informing workplace parties about the potential mismatches between job demands and the capability of their labour force. However, estimating occupational performance requires consideration of multiple factors that may govern capacity. In this paper, a novel model is described that uses a stochastic algorithm to estimate how variability in underlying biomechanical constraints affects hand force capability. In addition, the model estimates psychophysically acceptable hand force capacity thresholds by applying a biomechanical weakest link approach. Model estimates were tested against experimentally determined maximal and psychophysically determined hand forces in two exertion directions in constrained postures. The model underestimated maximum hand force capacity relative to measured maximum hand force by 30% and 35% during downward pressing and horizontal pulling, respectively. These values are consistent with those observed using previous two-dimensional models. Psychophysically acceptable hand forces were also underestimated by 29% during both pressing and pulling. Since the psychophysical estimates were scaled as a percentage of the estimated maximum capacity, this suggests that the underestimation in both predictions may be corrected by improving estimates of maximum hand force. Psychophysically acceptable forces were observed to be partially governed by demands at the biomechanical weakest link.